Yes to both - if it's a large clump, it'll need two of you with forks both to dig it up and then force the forks in and pull the clump into two sections for immediate replanting - prepare the planting holes first!
You may find that you need to take a sharp knife to it to cut through the middle of the clump!

Loosen the clump all around with your fork ... if not you can break the fork. If you can, have someone pulling on the upper part. A serrated bread knife works real well on cutting it apart.